The two small Pluto moons with temporary designations S/2005 P 1 and S/2005 P 2, discovered in mid-May 2005 with the Hubble Space Telescope (Weaver et. al., IAUC 8625), have now been named respectively Hydra and Nix by the IAU.

In Greek mythology Nyx was the goddess of darkness and the night, a very appropriate name for a moon orbiting Pluto - the god of the underworld. To avoid confusion with the asteroid (3908) Nyx, the Egyptian spelling Nix was chosen. Hydra is the serpent with nine heads that guarded the underworld.

Some people transliterate Greek upsilon as y, others as u, so Greek Νύξ is normally transliterated Nyx or Nux. Stephen Carlson has this to say about upsilon and iota in Egyptian papyri:

When did upsilon start unrounding to the sound of an iota? Egyptian papyri from the 2nd and 3rd centuries show a confusion of U and I, so this indicates that around that time, possibly a bit earlier, is when the U started converging to I, and that probably is a regional variation.

Pluto now has three known moons, Charon (discovered in 1978), Hydra, and Nix. Pluto is of course the god of the underworld, and Charon is the ferryman who transports the dead across the River Styx. The Hydra is among the beasts stationed at hell's gate, according to Vergil, Aeneid 6.285-289 (tr. H. Rushton Fairclough):

And many monstrous forms besides of various beasts are stalled at the doors, Centaurs and double-shaped Scyllas, and the hundredfold Briareus, and the beast of Lerna [Hydra], hissing horribly, and the Chimaera armed with flame, Gorgons and Harpies, and the shape of the three-bodied shade [Geryon].

Nyx was the goddess of night and the mother of Charon, the boatsman who takes souls across the River Styx and into Pluto's grasp.

Perhaps there is some ancient author who says that Nyx is Charon's mother, but I can't track one down. Hesiod (Theogony 211-225, tr. H.G. Evelyn-White) lists the children of Nyx, and Charon isn't among them:

And Night bore hateful Doom and black Fate and Death, and she bore Sleep and the tribe of Dreams. And again the goddess murky Night, though she lay with none, bare Blame and painful Woe, and the Hesperides who guard the rich, golden apples and the trees bearing fruit beyond glorious Ocean. Also she bore the Destinies and ruthless avenging Fates, Clotho and Lachesis and Atropos, who give men at their birth both evil and good to have, and they pursue the transgressions of men and of gods: and these goddesses never cease from their dread anger until they punish the sinner with a sore penalty. Also deadly Night bore Nemesis (Indignation) to afflict mortal men, and after her, Deceit and Friendship and hateful Age and hard-hearted Strife.

But Nyx has her dwelling in the underworld, according to Hesiod (Theogony 748), and therefore has as good a claim as any to be one of Pluto's moons.